Mr. Atheist, if you had your wish and all of the Christians in the United States suddenly joined you, the result would be that many charities would starve for funds. Other charities, schools, local governments, and other volunteer-based organizations would suffer as well...

So here is my question. What kind of warped morality would wish this upon a nation?

Again, we ought to examine Kaffinator's premise for veracity before accepting his conclusion.

"The differences in charity between secular and religious people are dramatic. Religious people are 25 percentage points more likely than secularists to donate money (91 percent to 66 percent) and 23 points more likely to volunteer time (67 percent to 44 percent)." [link]

First, in Brooks' work, he goes off on a tangent concerning what we are discussing here: Democrats and Republicans, Left and Right, and correlating those with "secular and religious". So it is a little difficult here to separate the various secularists from the various religionists, and that makes this source artice a little ambiguous. I mean, Buddhists may be either "secularists" or "religionists", depending on criteria, which Brooks does not clearly delineate overall. Each of the studies he cites use slightly different definitions and self-identification criteria to distinguish the groups.

Now, it has been amply demonstrated that aside from church attendance, factors like prayer and belief in God do not fall along "party lines". See here for more. The author wrongly conflates politics with religion, a fairly egregious intellectual error, especially considering the shifts of religious identification within parties over the decades, but let's stick to the topic...

That said, let's just consider Brooks' work as Kaff, and others, probably want it to be, and let "religious / people of faith" = Christian and "secular" = atheists. I will freely say at the outset that I find myself agreeing that persons of faith tend to be more charitable than those without, as a simple measure of reported giving of income to general non-profits, including, especially, their church. However, and I think this is important, how much of the money given to the average church goes for a charitable work?

Let us think for a moment about charity in effect versus charity in intent.

For instance, the fiercely secular AmeriCares reports that 99% of its income go to its programs! In fact, a secular organization I belong to, CFI, links to this charity for hurricane relief. Those who give $1 will see $0.99 go to help people there. On the other hand, the Red Cross, which is also secular, only sees $0.95 of every $1 go to the people, and there have been many accusations of corruption there. Furthermore, the CEO of the Red Cross pulls down $600K, which is a ridiculous salary for a charity admin. Given this information, I would much rather give to the Salvation Army before the Red Cross, and I could care the less that they are spreading what I consider to be a false message along with their help [although Charity Nav doesn't have data on them, since they don't have to file a 990], and to the AmeriCares organization before either one of them.

In this sense, we need to think about what you really want to do -- just evaluate people's giving, or evaluate the effect of that charity. I don't think you'd cry your eyes dry if corrupt and inefficient charities were bumped out and replaced by or subsumed by those of integrity and efficacy, secular or religious, would you? If you care about people, you wouldn't. If all you care about are the actions done [charity] and not what faith [or lack thereof] the acting parties maintain. So, at the outset, I would like a little clarity in your question -- do you want to ask us atheists what would happen if everyone became atheists, insofar as clothing the naked, feeding the hungry, sheltering the homeless, giving medical care to the sick, etc., are concerned, or insofar as churches are concerned? Because we will need to define "charity" and think about how churches relate to charity.

Now, in the case of the average church, the church maintains land, a building, insurance, a staff (sometimes a large staff as a ratio of parishoners), vehicles, and all the overhead associated with all of those things. In that sense, a realtively HUGE portion of every $1 given as a "tithe" goes to do nothing but serve "the church" and not someone in need. Let's be honest, here, most Christian giving is in tithes to their own church -- 10% of their income, according to the OT. If we want to look at how much that 10% can be considered charity, I would love to consider the argument anew. In fact, let's think about this for a moment -- every church in america shuts down tomorrow, every mosque, every house of worship of any kind. Now, suddenly, 10% of the income of 80-90% of the population (yes, I know this is estimating, but the gist remains) is free and available to be given to organizations which do nothing but feed the poor, clothe the naked, and bind up the wounds of the sick.

Hmmmm...this issue is a little more complicated than you want to make it out to be, isn't it?

So, let's look at what your study says about non-religious causes:Religious people are more generous than secular people with non-religious causes as well as with religious ones. While 68 percent of the total population gives (and 51 percent volunteers) to non-religious causes each year, religious people are 10 points more likely to give to these causes than secularists (71 percent to 61 percent) and 21 points more likely to volunteer (60 percent to 39 percent).

Now this is impressive, but for a totally different reason:
While Christians [and others] have a commandment from God to give, and fear of hell, and hope of heaven, to motivate them, a mere 10% difference is observed in what we can objectively call "pure charity work" insofar as money is concerned, and a slightly more substantial 21% in volunteering. Would you wave this as a banner of triumph for your religion? Pretty shoddy statistics to soapbox from, especially considering the organizational factor behind churches, etc., and that the prevalence of stay-at-home-moms among religionists is much higher than secularists, and thus more available volunteers to pool from, etc. Now, I won't defend those of us who are irreligious and have no empathy, nor rational self-interest extrapolated to altruism, as I believe it logically does. Those people who do not care for their fellow human beings, religious or nonreligious, are a blight to those of us who do, and those of us who will take care of these apathists through our giving and volunteering at some point in the future.

Back to the question at hand, though -- if all the churches in the country shut their doors tomorrow, would private schools and "pure charities" really suffer? Those people who already demonstrate their willingness to give without religious motivation would continue to do so, and it is logical to infer that those who are currently religious would follow the trend observed once the churches shut their doors -- that a sizable chunk of them would continue to give, if not nearly all of them. In fact, the sudden effluence of wealth created by the shutting of church doors would be available to do "pure charity work" = feeding, clothing, medical care, etc., with no "strings attached".

So, your burden is, at this point, to rationalize how any people would actually suffer a loss of food, clothes, or medical care if all churches were shut down tomorrow, and to consider your own question carefully, and perhaps to rephrase it to be more specific. Atheists and other secularists really have an onus to do a better job in organizing and making a public spectacle of their giving, to "rally the troops", and to continue to maintain the moral high ground that we have: when we do good, it is unquestionably and unequivocally because we care, have compassion for, and empathy for, our fellow human beings, and not for hope of reward [heaven], fear of punishment [hell], or the prodding and guilt trip of a pastor.

Thus the issue is not as clear-cut as you would have it, and I will concede that secularists/atheists need to do a better job of promoting naturally-grounded ethics and morality and charity [humanists do a pretty good job here, but we need a broader front]. So do some more research and thinking, and please reformulate your question to consider the effects of charity, versus the facade of charity [church/tithing].

The latter resource is most useful only if you are a member, write off and send $3 for a written report, or if you just want the top-rated charities. The reason is that they don't report this information freely on their website for every charity they research.